A359710 Order of shifts of Thue-Morse sequence.

0, 1, 3, 0, 2, 1, 5, 3, 6, 0, 4, 2, 7, 1, 9, 5, 15, 3, 10, 6, 12, 0, 8, 4, 14, 2, 11, 7, 13, 1, 17, 9, 29, 5, 23, 15, 27, 3, 18, 10, 30, 6, 20, 12, 24, 0, 16, 8, 28, 4, 22, 14, 26, 2, 19, 11, 31, 7, 21, 13, 25, 1, 33, 17, 57, 9, 45, 29, 53, 5, 39, 23, 63, 15

Offset

1,3

Comments

Let t_i be the Thue-Morse (A010060) sequence shifted by i symbols. Say t_i < t_j if t_i precedes t_j in lexicographic order. Then the paper of Cheng shows t_0 < t_1, t_3 < t_0 < t_2 < t_1, t_5 < t_3 < t_6 < t_0 < t_4 < t_2 < t_7 < t_1, etc. Concatenating all these together gives the sequence in question.

Links

Table of n, a(n) for n=1..74.

Yin Choi Cheng, Order types of shifts of morphic words, INTEGERS 23 (2023), Paper #A1.

Crossrefs

Cf. A010060.

Sequence in context: A034389 A084196 A295041 * A127913 A135991 A331422

Adjacent sequences: A359707 A359708 A359709 * A359711 A359712 A359713

Keyword

nonn

Author

Jeffrey Shallit, Jan 11 2023

Status

approved